Radiative transfer of synchrotron radiation through a compressed random magnetic field

Abstract

The generally low polarization levels present in extragalactic radio sources suggest magnetic fields that are largely turbulent, presumably maintained by turbulence motion of the underlying plasma. The polarization of radio emission is often generated as the plasma is compressed by shock waves, and this type of configuration has been widely applied, from the cores of AGN to the lobes of classical double radio sources. Here we note that, in the absence of Faraday rotation, the synchrotron radiative transfer equations for such a configuration, separate, leading to relatively simple solutions for opaque or partially opaque sources. Expressions for the emission and absorption coefficients are derived, and, although in general, these must be evaluated numerically, the process is much simpler than a full numerical solution of the transfer equations.